We study the structure of the group of equivariant Lipschitz
homeomorphisms of a smooth $G$ -manifold $M$ which are isotopic
to the identity through equivariant Lipschitz homeomorphisms
with compact support. First we show that the group is perfect
when $M$ is a smooth free $G$ -manifold. Secondly in the case of
$\mathbf{C}^n$ with the canonical $U(n)$ -action, we show that the first homology group admits continuous moduli. Thirdly we apply the result to the case of the group $L(\mathbf{C},0)$ of Lipschitz homeomorphisms of $\mathbf{C}^n$ fixing the origin.
@article{1145287091,
author = {ABE, K\=ojun and FUKUI, Kazuhiko and MIURA, Takeshi},
title = {On the first homology of the group of equivariant Lipschitz homeomorphisms},
journal = {J. Math. Soc. Japan},
volume = {58},
number = {3},
year = {2006},
pages = { 1-15},
language = {en},
url = {http://dml.mathdoc.fr/item/1145287091}
}
ABE, Kōjun; FUKUI, Kazuhiko; MIURA, Takeshi. On the first homology of the group of equivariant Lipschitz homeomorphisms. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp. 1-15. http://gdmltest.u-ga.fr/item/1145287091/